Wess-Zumino-Witten action and photons from the Chiral Magnetic Effect

We revisit the Chiral Magnetic Effect (CME) using the chiral Lagrangian. We demonstrate that the electric-current formula of the CME is derived immediately from the contact part of the Wess-Zumino-Witten action. This implies that the CME could be, if observed, a signature for the local parity violation, but a direct evidence for neither quark deconfinement nor chiral restoration. We also discuss the reverse Chiral Magnetic Primakoff Effect, i.e. the real photon production through the vertex associated with the CME, which is kinematically possible for space-time inhomogeneous configurations of magnetic fields and the strong theta angle. We make a qualitative estimate for the photon yield to find that it comparable to the thermal photon.